The yaw angle Ψ is defined as the angle between the longitudinal axis of the vehicle and an axis parallel to the surface of the earth in an earth-fixed coordinate system.
The slip angle β is the angle between the speed vector of a point secured to the vehicle (i.e. the vehicle's centre of gravity) and the longitudinal axis of the vehicle. Longitudinal and lateral inclination are acquired by the pitch angle θ and roll angle φ of the vehicle. Roll, pitch and yaw angles are defined to DIN 70000.
The actual horizontal orientation of the vehicle, which is acquired by way of the yaw angle, can be used for rapid route determination in vehicle navigation but it is primarily important in this connection as an auxiliary quantity in slip angle determination. The slip angle provides information about the vehicle orientation with respect to the direction of movement and constitutes a measure of the lateral slippage of the vehicle so to speak. If side slippage of the vehicle occurs, the vehicle usually leaves its stable driving condition and enters a dangerous situation which potentially overtaxes the driver.
Optimally exact knowledge of the yaw and slip angles therefore means that such dangerous situations can be quickly recognized, and this in turn allows fast, electronically controlled intervention in the driving situation with the aid of electrically controllable actuators, for example of the drive train, braking system, steering, suspension/damping, etc., and therewith automatic stabilization of the vehicle. This represents a fundamental contribution to driving safety in borderline and dangerous situations.
The yaw angle of a vehicle is conventionally determined in the presence of a yaw rate sensor by integration of the yaw rate signal. Such yaw rate sensors (gyroscopes) may nowadays be produced with properties suitable for a vehicle at comparatively low cost and are already available in vehicles with electronic stability programs, ESP, or navigation systems.
Problems with this determination of the yaw angle frequently result for example as a result of temperature-dependent value differences (offsets) in the yaw rate signals which cause an error in the integration of the yaw angle that increases at least linearly over time. Time-dependent drifts of the offsets as well as falsification of the results by carriageway gradients also lead to an additional increase in the integration error. The difference in the calculated yaw angle from the actual yaw angle therefore increases continuously. This can lead to misinterpretations of the actual driving situation and in the worst case even to incorrect interventions in vehicle control.
Alternatively the yaw angle may be obtained by evaluating the wheel speed sensors that always exist in vehicles with antilock braking systems, ABS, and, if present, a steering angle sensor or steering wheel sensor. The main problem of this method is the wheel slippage, in particular side slippage, wheel properties such as the dynamic wheel radius in particular must be known and an increasing error occurs here as well owing to integration offsets.
A satellite-assisted positioning system (for example GPS) may also be used to determine the yaw angle, as is disclosed in documents U.S. Pat. No. 5,983,161 and U.S. Pat. No. 6,275,7773. However, for this either at least two aerials are required at different points of the vehicle that are as far apart as possible respectively. In the case of two or more GPS aerials in one vehicle orientation of the vehicle on the carriageway may be determined from the relative positions of the aerials in the earth-fixed system. In this case the absolute accuracy of the position determination imposes limits and such a solution is also not very practicable for cost reasons.
A further possibility lies in the fact that the angle of the speed vector of the vehicle, supplied by the GPS receiver, with respect to an earth-fixed axis is approximately equated to the yaw angle. However, this is no longer possible with increasing slip angles, i.e. precisely in a dangerous situation.
The slip angle is conventionally determined by the forces acting on the individual wheels, in particular the lateral forces. With the driving condition sensor systems that are conventionally present in current medium-size vehicles the lateral forces may be determined only inexactly and this method can only be applied in the case of small slip angles (<1-2°). With large slip angles the lateral acceleration, yaw rate and speed of the vehicle are conventionally used to determine the slip angle. Integration over the generally small difference of two large numbers is necessary in this case. Offsets of lateral acceleration and yaw rate sensors and falsification of the lateral acceleration values by transverse gradients of the carriageway can lead to significant errors in this connection. The existing sensor noise leads, moreover, to increasing integration errors when determining the slip angle.
Application US 2002/0198655 A1 proposes use of a satellite-assisted position determining system for determining the slip angle. The slip angle is determined as the difference between the direction of the speed vector of the vehicle and the orientation of the longitudinal axis of the vehicle, i.e. the yaw angle. However this method is only practicable if the yaw angle of the vehicle can be determined with adequate precision. Where only one GPS aerial exists but no additional surroundings sensor system, integrating methods would have to be used which, as already discussed, lead to offsets.
Finally, publication DE 10327695 A1 proposes determining the slip angle by way of a lane recognition system. The sensor system required for this is expensive and therefore exists in only a small number of vehicles.
There is the drawback in the described solutions that the required accuracy is not permanently ensured when determining the yaw and slip angles. Using additional and necessary sensor systems makes the available systems expensive and therefore unsuitable for use in a wide range of vehicles, including in the lower price categories.